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element_class_hexahedron_20_inline_impl.cc
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rAKA akantu
element_class_hexahedron_20_inline_impl.cc
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/**
* @file element_class_hexahedron_20_inline_impl.cc
*
* @author Mauro Corrado <mauro.corrado@epfl.ch>
* @author Sacha Laffely <sacha.laffely@epfl.ch>
* @author Damien Scantamburlo <damien.scantamburlo@epfl.ch>
*
* @date creation: Tue Mar 31 2015
* @date last modification: Thu Jul 16 2015
*
* @brief Specialization of the element_class class for the type _hexahedron_20
*
* @section LICENSE
*
* Copyright (©) 2015 EPFL (Ecole Polytechnique Fédérale de Lausanne) Laboratory
* (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
* @section DESCRIPTION
*
* @verbatim
\y
\z /
| /
7-----|18--------6
/| | / /|
/ | | / / |
19 | | / 17 |
/ 15 | / / 14
/ | | / / |
4-------16---/---5 |
| | +----|------------\x
| 3-------10-|-----2
| / | /
12 / 13 /
| 11 | 9
| / | /
|/ |/
0--------8-------1
x y z
* N0 -1 -1 -1
* N1 1 -1 -1
* N2 1 1 -1
* N3 -1 1 -1
* N4 -1 -1 1
* N5 1 -1 1
* N6 1 1 1
* N7 -1 1 1
* N8 0 -1 -1
* N9 1 0 -1
* N10 0 1 -1
* N11 -1 0 -1
* N12 -1 -1 0
* N13 1 -1 0
* N14 1 1 0
* N15 -1 1 0
* N16 0 -1 1
* N17 1 0 1
* N18 0 1 1
* N19 -1 0 1
*/
/* -------------------------------------------------------------------------- */
AKANTU_DEFINE_ELEMENT_CLASS_PROPERTY
(
_hexahedron_20
,
_gt_hexahedron_20
,
_itp_serendip_hexahedron_20
,
_ek_regular
,
3
,
_git_segment
,
3
);
AKANTU_DEFINE_SHAPE
(
_gt_hexahedron_20
,
_gst_square
);
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
>
inline
void
InterpolationElement
<
_itp_serendip_hexahedron_20
>::
computeShapes
(
const
vector_type
&
c
,
vector_type
&
N
)
{
// Shape function , Natural coordinates
N
(
0
)
=
0.125
*
(
1
-
c
(
0
))
*
(
1
-
c
(
1
))
*
(
1
-
c
(
2
))
*
(
-
2
-
c
(
0
)
-
c
(
1
)
-
c
(
2
));
N
(
1
)
=
0.125
*
(
1
+
c
(
0
))
*
(
1
-
c
(
1
))
*
(
1
-
c
(
2
))
*
(
-
2
+
c
(
0
)
-
c
(
1
)
-
c
(
2
));
N
(
2
)
=
0.125
*
(
1
+
c
(
0
))
*
(
1
+
c
(
1
))
*
(
1
-
c
(
2
))
*
(
-
2
+
c
(
0
)
+
c
(
1
)
-
c
(
2
));
N
(
3
)
=
0.125
*
(
1
-
c
(
0
))
*
(
1
+
c
(
1
))
*
(
1
-
c
(
2
))
*
(
-
2
-
c
(
0
)
+
c
(
1
)
-
c
(
2
));
N
(
4
)
=
0.125
*
(
1
-
c
(
0
))
*
(
1
-
c
(
1
))
*
(
1
+
c
(
2
))
*
(
-
2
-
c
(
0
)
-
c
(
1
)
+
c
(
2
));
N
(
5
)
=
0.125
*
(
1
+
c
(
0
))
*
(
1
-
c
(
1
))
*
(
1
+
c
(
2
))
*
(
-
2
+
c
(
0
)
-
c
(
1
)
+
c
(
2
));
N
(
6
)
=
0.125
*
(
1
+
c
(
0
))
*
(
1
+
c
(
1
))
*
(
1
+
c
(
2
))
*
(
-
2
+
c
(
0
)
+
c
(
1
)
+
c
(
2
));
N
(
7
)
=
0.125
*
(
1
-
c
(
0
))
*
(
1
+
c
(
1
))
*
(
1
+
c
(
2
))
*
(
-
2
-
c
(
0
)
+
c
(
1
)
+
c
(
2
));
N
(
8
)
=
0.25
*
(
1
-
c
(
0
)
*
c
(
0
))
*
(
1
-
c
(
1
))
*
(
1
-
c
(
2
));
N
(
9
)
=
0.25
*
(
1
-
c
(
1
)
*
c
(
1
))
*
(
1
+
c
(
0
))
*
(
1
-
c
(
2
));
N
(
10
)
=
0.25
*
(
1
-
c
(
0
)
*
c
(
0
))
*
(
1
+
c
(
1
))
*
(
1
-
c
(
2
));
N
(
11
)
=
0.25
*
(
1
-
c
(
1
)
*
c
(
1
))
*
(
1
-
c
(
0
))
*
(
1
-
c
(
2
));
N
(
12
)
=
0.25
*
(
1
-
c
(
2
)
*
c
(
2
))
*
(
1
-
c
(
0
))
*
(
1
-
c
(
1
));
N
(
13
)
=
0.25
*
(
1
-
c
(
2
)
*
c
(
2
))
*
(
1
+
c
(
0
))
*
(
1
-
c
(
1
));
N
(
14
)
=
0.25
*
(
1
-
c
(
2
)
*
c
(
2
))
*
(
1
+
c
(
0
))
*
(
1
+
c
(
1
));
N
(
15
)
=
0.25
*
(
1
-
c
(
2
)
*
c
(
2
))
*
(
1
-
c
(
0
))
*
(
1
+
c
(
1
));
N
(
16
)
=
0.25
*
(
1
-
c
(
0
)
*
c
(
0
))
*
(
1
-
c
(
1
))
*
(
1
+
c
(
2
));
N
(
17
)
=
0.25
*
(
1
-
c
(
1
)
*
c
(
1
))
*
(
1
+
c
(
0
))
*
(
1
+
c
(
2
));
N
(
18
)
=
0.25
*
(
1
-
c
(
0
)
*
c
(
0
))
*
(
1
+
c
(
1
))
*
(
1
+
c
(
2
));
N
(
19
)
=
0.25
*
(
1
-
c
(
1
)
*
c
(
1
))
*
(
1
-
c
(
0
))
*
(
1
+
c
(
2
));
}
/* -------------------------------------------------------------------------- */
template
<>
template
<
class
vector_type
,
class
matrix_type
>
inline
void
InterpolationElement
<
_itp_serendip_hexahedron_20
>::
computeDNDS
(
const
vector_type
&
c
,
matrix_type
&
dnds
)
{
//derivatives
//ddx
dnds
(
0
,
0
)
=
0.25
*
(
c
(
0
)
+
0.5
*
(
c
(
1
)
+
c
(
2
)
+
1
))
*
(
c
(
1
)
-
1
)
*
(
c
(
2
)
-
1
);
dnds
(
0
,
1
)
=
0.25
*
(
c
(
0
)
-
0.5
*
(
c
(
1
)
+
c
(
2
)
+
1
))
*
(
c
(
1
)
-
1
)
*
(
c
(
2
)
-
1
);
dnds
(
0
,
2
)
=
-
0.25
*
(
c
(
0
)
+
0.5
*
(
c
(
1
)
-
c
(
2
)
-
1
))
*
(
c
(
1
)
+
1
)
*
(
c
(
2
)
-
1
);
dnds
(
0
,
3
)
=
-
0.25
*
(
c
(
0
)
-
0.5
*
(
c
(
1
)
-
c
(
2
)
-
1
))
*
(
c
(
1
)
+
1
)
*
(
c
(
2
)
-
1
);
dnds
(
0
,
4
)
=
-
0.25
*
(
c
(
0
)
+
0.5
*
(
c
(
1
)
-
c
(
2
)
+
1
))
*
(
c
(
1
)
-
1
)
*
(
c
(
2
)
+
1
);
dnds
(
0
,
5
)
=
-
0.25
*
(
c
(
0
)
-
0.5
*
(
c
(
1
)
-
c
(
2
)
+
1
))
*
(
c
(
1
)
-
1
)
*
(
c
(
2
)
+
1
);
dnds
(
0
,
6
)
=
0.25
*
(
c
(
0
)
+
0.5
*
(
c
(
1
)
+
c
(
2
)
-
1
))
*
(
c
(
1
)
+
1
)
*
(
c
(
2
)
+
1
);
dnds
(
0
,
7
)
=
0.25
*
(
c
(
0
)
-
0.5
*
(
c
(
1
)
+
c
(
2
)
-
1
))
*
(
c
(
1
)
+
1
)
*
(
c
(
2
)
+
1
);
dnds
(
0
,
8
)
=
-
0.5
*
c
(
0
)
*
(
c
(
1
)
-
1
)
*
(
c
(
2
)
-
1
);
dnds
(
0
,
9
)
=
0.25
*
(
c
(
1
)
*
c
(
1
)
-
1
)
*
(
c
(
2
)
-
1
);
dnds
(
0
,
10
)
=
0.5
*
c
(
0
)
*
(
c
(
1
)
+
1
)
*
(
c
(
2
)
-
1
);
dnds
(
0
,
11
)
=
-
0.25
*
(
c
(
1
)
*
c
(
1
)
-
1
)
*
(
c
(
2
)
-
1
);
dnds
(
0
,
12
)
=
-
0.25
*
(
c
(
2
)
*
c
(
2
)
-
1
)
*
(
c
(
1
)
-
1
);
dnds
(
0
,
13
)
=
0.25
*
(
c
(
1
)
-
1
)
*
(
c
(
2
)
*
c
(
2
)
-
1
);
dnds
(
0
,
14
)
=
-
0.25
*
(
c
(
1
)
+
1
)
*
(
c
(
2
)
*
c
(
2
)
-
1
);
dnds
(
0
,
15
)
=
0.25
*
(
c
(
1
)
+
1
)
*
(
c
(
2
)
*
c
(
2
)
-
1
);
dnds
(
0
,
16
)
=
0.5
*
c
(
0
)
*
(
c
(
1
)
-
1
)
*
(
c
(
2
)
+
1
);
dnds
(
0
,
17
)
=
-
0.25
*
(
c
(
2
)
+
1
)
*
(
c
(
1
)
*
c
(
1
)
-
1
);
dnds
(
0
,
18
)
=
-
0.5
*
c
(
0
)
*
(
c
(
1
)
+
1
)
*
(
c
(
2
)
+
1
);
dnds
(
0
,
19
)
=
0.25
*
(
c
(
2
)
+
1
)
*
(
c
(
1
)
*
c
(
1
)
-
1
);
//ddy
dnds
(
1
,
0
)
=
0.25
*
(
c
(
1
)
+
0.5
*
(
c
(
0
)
+
c
(
2
)
+
1
))
*
(
c
(
0
)
-
1
)
*
(
c
(
2
)
-
1
);
dnds
(
1
,
1
)
=
-
0.25
*
(
c
(
1
)
-
0.5
*
(
c
(
0
)
-
c
(
2
)
-
1
))
*
(
c
(
0
)
+
1
)
*
(
c
(
2
)
-
1
);
dnds
(
1
,
2
)
=
-
0.25
*
(
c
(
1
)
+
0.5
*
(
c
(
0
)
-
c
(
2
)
-
1
))
*
(
c
(
0
)
+
1
)
*
(
c
(
2
)
-
1
);
dnds
(
1
,
3
)
=
0.25
*
(
c
(
1
)
-
0.5
*
(
c
(
0
)
+
c
(
2
)
+
1
))
*
(
c
(
0
)
-
1
)
*
(
c
(
2
)
-
1
);
dnds
(
1
,
4
)
=
-
0.25
*
(
c
(
1
)
+
0.5
*
(
c
(
0
)
-
c
(
2
)
+
1
))
*
(
c
(
0
)
-
1
)
*
(
c
(
2
)
+
1
);
dnds
(
1
,
5
)
=
0.25
*
(
c
(
1
)
-
0.5
*
(
c
(
0
)
+
c
(
2
)
-
1
))
*
(
c
(
0
)
+
1
)
*
(
c
(
2
)
+
1
);
dnds
(
1
,
6
)
=
0.25
*
(
c
(
1
)
+
0.5
*
(
c
(
0
)
+
c
(
2
)
-
1
))
*
(
c
(
0
)
+
1
)
*
(
c
(
2
)
+
1
);
dnds
(
1
,
7
)
=
-
0.25
*
(
c
(
1
)
-
0.5
*
(
c
(
0
)
-
c
(
2
)
+
1
))
*
(
c
(
0
)
-
1
)
*
(
c
(
2
)
+
1
);
dnds
(
1
,
8
)
=
-
0.25
*
(
c
(
0
)
*
c
(
0
)
-
1
)
*
(
c
(
2
)
-
1
);
dnds
(
1
,
9
)
=
0.5
*
c
(
1
)
*
(
c
(
0
)
+
1
)
*
(
c
(
2
)
-
1
);
dnds
(
1
,
10
)
=
0.25
*
(
c
(
0
)
*
c
(
0
)
-
1
)
*
(
c
(
2
)
-
1
);
dnds
(
1
,
11
)
=
-
0.5
*
c
(
1
)
*
(
c
(
0
)
-
1
)
*
(
c
(
2
)
-
1
);
dnds
(
1
,
12
)
=
-
0.25
*
(
c
(
2
)
*
c
(
2
)
-
1
)
*
(
c
(
0
)
-
1
);
dnds
(
1
,
13
)
=
0.25
*
(
c
(
0
)
+
1
)
*
(
c
(
2
)
*
c
(
2
)
-
1
);
dnds
(
1
,
14
)
=
-
0.25
*
(
c
(
0
)
+
1
)
*
(
c
(
2
)
*
c
(
2
)
-
1
);
dnds
(
1
,
15
)
=
0.25
*
(
c
(
0
)
-
1
)
*
(
c
(
2
)
*
c
(
2
)
-
1
);
dnds
(
1
,
16
)
=
0.25
*
(
c
(
2
)
+
1
)
*
(
c
(
0
)
*
c
(
0
)
-
1
);
dnds
(
1
,
17
)
=
-
0.5
*
c
(
1
)
*
(
c
(
0
)
+
1
)
*
(
c
(
2
)
+
1
);
dnds
(
1
,
18
)
=
-
0.25
*
(
c
(
2
)
+
1
)
*
(
c
(
0
)
*
c
(
0
)
-
1
);
dnds
(
1
,
19
)
=
0.5
*
c
(
1
)
*
(
c
(
0
)
-
1
)
*
(
c
(
2
)
+
1
);
//ddz
dnds
(
2
,
0
)
=
0.25
*
(
c
(
2
)
+
0.5
*
(
c
(
0
)
+
c
(
1
)
+
1
))
*
(
c
(
0
)
-
1
)
*
(
c
(
1
)
-
1
);
dnds
(
2
,
1
)
=
-
0.25
*
(
c
(
2
)
-
0.5
*
(
c
(
0
)
-
c
(
1
)
-
1
))
*
(
c
(
0
)
+
1
)
*
(
c
(
1
)
-
1
);
dnds
(
2
,
2
)
=
0.25
*
(
c
(
2
)
-
0.5
*
(
c
(
0
)
+
c
(
1
)
-
1
))
*
(
c
(
0
)
+
1
)
*
(
c
(
1
)
+
1
);
dnds
(
2
,
3
)
=
-
0.25
*
(
c
(
2
)
+
0.5
*
(
c
(
0
)
-
c
(
1
)
+
1
))
*
(
c
(
0
)
-
1
)
*
(
c
(
1
)
+
1
);
dnds
(
2
,
4
)
=
0.25
*
(
c
(
2
)
-
0.5
*
(
c
(
0
)
+
c
(
1
)
+
1
))
*
(
c
(
0
)
-
1
)
*
(
c
(
1
)
-
1
);
dnds
(
2
,
5
)
=
-
0.25
*
(
c
(
2
)
+
0.5
*
(
c
(
0
)
-
c
(
1
)
-
1
))
*
(
c
(
0
)
+
1
)
*
(
c
(
1
)
-
1
);
dnds
(
2
,
6
)
=
0.25
*
(
c
(
2
)
+
0.5
*
(
c
(
0
)
+
c
(
1
)
-
1
))
*
(
c
(
0
)
+
1
)
*
(
c
(
1
)
+
1
);
dnds
(
2
,
7
)
=
-
0.25
*
(
c
(
2
)
-
0.5
*
(
c
(
0
)
-
c
(
1
)
+
1
))
*
(
c
(
0
)
-
1
)
*
(
c
(
1
)
+
1
);
dnds
(
2
,
8
)
=
-
0.25
*
(
c
(
0
)
*
c
(
0
)
-
1
)
*
(
c
(
1
)
-
1
);
dnds
(
2
,
9
)
=
0.25
*
(
c
(
1
)
*
c
(
1
)
-
1
)
*
(
c
(
0
)
+
1
);
dnds
(
2
,
10
)
=
0.25
*
(
c
(
0
)
*
c
(
0
)
-
1
)
*
(
c
(
1
)
+
1
);
dnds
(
2
,
11
)
=
-
0.25
*
(
c
(
1
)
*
c
(
1
)
-
1
)
*
(
c
(
0
)
-
1
);
dnds
(
2
,
12
)
=
-
0.5
*
c
(
2
)
*
(
c
(
1
)
-
1
)
*
(
c
(
0
)
-
1
);
dnds
(
2
,
13
)
=
0.5
*
c
(
2
)
*
(
c
(
0
)
+
1
)
*
(
c
(
1
)
-
1
);
dnds
(
2
,
14
)
=
-
0.5
*
c
(
2
)
*
(
c
(
0
)
+
1
)
*
(
c
(
1
)
+
1
);
dnds
(
2
,
15
)
=
0.5
*
c
(
2
)
*
(
c
(
0
)
-
1
)
*
(
c
(
1
)
+
1
);
dnds
(
2
,
16
)
=
0.25
*
(
c
(
1
)
-
1
)
*
(
c
(
0
)
*
c
(
0
)
-
1
);
dnds
(
2
,
17
)
=
-
0.25
*
(
c
(
0
)
+
1
)
*
(
c
(
1
)
*
c
(
1
)
-
1
);
dnds
(
2
,
18
)
=
-
0.25
*
(
c
(
1
)
+
1
)
*
(
c
(
0
)
*
c
(
0
)
-
1
);
dnds
(
2
,
19
)
=
0.25
*
(
c
(
0
)
-
1
)
*
(
c
(
1
)
*
c
(
1
)
-
1
);
}
/* -------------------------------------------------------------------------- */
template
<>
inline
Real
GeometricalElement
<
_gt_hexahedron_20
>::
getInradius
(
const
Matrix
<
Real
>
&
coord
)
{
Vector
<
Real
>
u0
=
coord
(
0
);
Vector
<
Real
>
u1
=
coord
(
1
);
Vector
<
Real
>
u2
=
coord
(
2
);
Vector
<
Real
>
u3
=
coord
(
3
);
Vector
<
Real
>
u4
=
coord
(
4
);
Vector
<
Real
>
u5
=
coord
(
5
);
Vector
<
Real
>
u6
=
coord
(
6
);
Vector
<
Real
>
u7
=
coord
(
7
);
Vector
<
Real
>
u8
=
coord
(
8
);
Vector
<
Real
>
u9
=
coord
(
9
);
Vector
<
Real
>
u10
=
coord
(
10
);
Vector
<
Real
>
u11
=
coord
(
11
);
Vector
<
Real
>
u12
=
coord
(
12
);
Vector
<
Real
>
u13
=
coord
(
13
);
Vector
<
Real
>
u14
=
coord
(
14
);
Vector
<
Real
>
u15
=
coord
(
15
);
Vector
<
Real
>
u16
=
coord
(
16
);
Vector
<
Real
>
u17
=
coord
(
17
);
Vector
<
Real
>
u18
=
coord
(
18
);
Vector
<
Real
>
u19
=
coord
(
19
);
Real
a
=
u0
.
distance
(
u1
);
Real
b
=
u1
.
distance
(
u2
);
Real
c
=
u2
.
distance
(
u3
);
Real
d
=
u3
.
distance
(
u0
);
Real
e
=
u0
.
distance
(
u4
);
Real
f
=
u1
.
distance
(
u5
);
Real
g
=
u2
.
distance
(
u6
);
Real
h
=
u3
.
distance
(
u7
);
Real
i
=
u4
.
distance
(
u5
);
Real
j
=
u5
.
distance
(
u6
);
Real
k
=
u6
.
distance
(
u7
);
Real
l
=
u7
.
distance
(
u4
);
Real
x
=
std
::
min
(
a
,
std
::
min
(
b
,
std
::
min
(
c
,
d
)));
Real
y
=
std
::
min
(
e
,
std
::
min
(
f
,
std
::
min
(
g
,
h
)));
Real
z
=
std
::
min
(
i
,
std
::
min
(
j
,
std
::
min
(
k
,
l
)));
Real
p
=
std
::
min
(
x
,
std
::
min
(
y
,
z
));
return
p
;
}
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